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## Details

Genre/Form: | Electronic books |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Daisuke Takahashi |

ISBN: | 9789811399657 9811399654 |

OCLC Number: | 1122680860 |

Description: | 1 online resource (ix, 114 pages) : illustrations |

Contents: | Intro; Preface; Contents; 1 Introduction; References; 2 Fast Fourier Transform; 2.1 Definitions of DFT; 2.2 Basic Idea of FFT; 2.3 Cooley-Tukey FFT Algorithm; 2.4 Bit-Reversal Permutation; 2.5 Stockham FFT Algorithm; 2.6 FFT Algorithm for Real Data; 2.6.1 FFT of Two Real Data Simultaneously; 2.6.2 n-Point Real FFT Using n/2-Point Complex FFT; References; 3 Mixed-Radix FFT Algorithms; 3.1 Two-Dimensional Formulation of DFT; 3.2 Radix-3 FFT Algorithm; 3.3 Radix-4 FFT Algorithm; 3.4 Radix-5 FFT Algorithm; 3.5 Radix-8 FFT Algorithm; References; 4 Split-Radix FFT Algorithms 4.1 Split-Radix FFT Algorithm4.2 Extended Split-Radix FFT Algorithm; References; 5 Multidimensional FFT Algorithms; 5.1 Definition of Two-Dimensional DFT; 5.2 Two-Dimensional FFT Algorithm; 5.3 Definition of Three-Dimensional DFT; 5.4 Three-Dimensional FFT Algorithm; Reference; 6 High-Performance FFT Algorithms; 6.1 Four-Step FFT Algorithm; 6.2 Five-Step FFT Algorithm; 6.3 Six-Step FFT Algorithm; 6.4 Blocked Six-Step FFT Algorithm; 6.5 Nine-Step FFT Algorithm; 6.6 Recursive Six-Step FFT Algorithm; 6.7 Blocked Multidimensional FFT Algorithms; 6.7.1 Blocked Two-Dimensional FFT Algorithm 6.7.2 Blocked Three-Dimensional FFT Algorithm6.8 FFT Algorithms Suitable for Fused Multiply-Add (FMA) Instructions; 6.8.1 Introduction; 6.8.2 FFT Kernel; 6.8.3 Goedecker's Technique; 6.8.4 Radix-16 FFT Algorithm; 6.8.5 Radix-16 FFT Algorithm Suitable for Fused Multiply-Add Instructions; 6.8.6 Evaluation; 6.9 FFT Algorithms for SIMD Instructions; 6.9.1 Introduction; 6.9.2 Vectorization of FFT Kernels Using Intel SSE3 Instructions; 6.9.3 Vectorization of FFT Kernels Using Intel AVX-512 Instructions; References; 7 Parallel FFT Algorithms for Shared-Memory Parallel Computers 7.1 Implementation of Parallel One-Dimensional FFT on Shared-Memory Parallel Computers7.1.1 Introduction; 7.1.2 A Recursive Three-Step FFT Algorithm; 7.1.3 Parallelization of Recursive Three-Step FFT; 7.2 Optimizing Parallel FFTs for Manycore Processors; 7.2.1 Introduction; 7.2.2 Parallelization of Six-Step FFT; 7.2.3 Performance Results; References; 8 Parallel FFT Algorithms for Distributed-Memory Parallel Computers; 8.1 Implementation of Parallel FFTs in Distributed-Memory Parallel Computers; 8.1.1 Parallel One-Dimensional FFT Using Block Distribution 8.1.2 Parallel One-Dimensional FFT Using Cyclic Distribution8.1.3 Parallel Two-Dimensional FFT in Distributed-Memory Parallel Computers; 8.1.4 Parallel Three-Dimensional FFT in Distributed-Memory Parallel Computers; 8.2 Computation-Communication Overlap for Parallel One-Dimensional FFT; 8.2.1 Introduction; 8.2.2 Computation-Communication Overlap; 8.2.3 Automatic Tuning of Parallel One-Dimensional FFT; 8.2.4 Performance Results; 8.3 Parallel Three-Dimensional FFT Using Two-Dimensional Decomposition; 8.3.1 Introduction |

Series Title: | High-performance computing series, v. 2 |

Responsibility: | Daisuke Takahashi. |

### Abstract:

Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. Chapter 5 explains multi-dimensional FFT algorithms, Chapter 6 presents high-performance FFT algorithms, and Chapter 7 addresses parallel FFT algorithms for shared-memory parallel computers.
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